A Parallel Variational Multiscale Method for Incompressible Flows Based on the Partition of Unity

Abstract

A parallel variational multiscale method based on the partition of unity is proposed for incompressible flows in this paper. Based on two-grid method, this algorithm localizes the global residual problem of variational multiscale method into a series of local linearized residual problems. To decrease the undesirable effect of the artificial homogeneous Dirichlet boundary condition of local sub-problems, an oversampling technique is also introduced. The globally continuous finite element solutions are constructed by assembling all local solutions together using the partition of unity functions. Numerical simulations demonstrate the high efficiency and flexibility of the new algorithm.